Potential energy surfaces, calculation pseudopotential

Fig. 5. Contour plot of the adiabatic potential-energy surface of an H atom in the (110) plane for the neutral H—B pair from a local-density pseudopotential calculation. The boron atom is at the center. For every hydrogen position, the B and Si atoms are allowed to relax, but only unrelaxed positions are indicated in the figure (Reprinted with permission from the American Physical Society, Denteneer, P.J.H., Van de Walle, C.G., and Pantelides, S.T. (1989). Phys. Rev. B 39, 10809.)...

As is well known, the vibrational Hamiltonian defined in internal coordinates may be written as the sum of three different terms the kinetic energy operator, the Potential Energy Surface and the V pseudopotential [1-3]. V is a kinetic energy term that arises when the classic vibrational Hamiltonian in non-Cartesian coordinates is transformed into the quantum-mechanical operator using the Podolsky trick [4]. The determination of V is a long process which requires the calculation of the molecular geometry and the derivatives of various structural parameters. 

The equilibrium geometries of Cp2M (M = Yb, Eu, Sm) were studied by ab initio pseudopotential calculations at the Hartree-Fock (HF), MP2 and CSID levels. In the Hartree-Fock calculations [118] all the metallocenes favoured regular sandwich-type equilibrium structures with increasingly shallow potential energy surfaces for the bending motions along the series, M = Ca, Yb, Sr, Eu, Sm, and Ba. 

In the present work, we report DFT calculations of hydrocarbons adsorption on Au2o cluster [4]. All calculations were carried out with the nonempirical local PBE (Perdew—Burke—Ernzerhof) functional, which we have used earlier in the study of gold complexes [5]. Calculations were performed with a PRIRODA software [6]. The basis set with the SBK pseudopotential was used [7]. In this pseudopotential, the outer electronic shells are described by the following basis sets H [311/1], C [311/311/11] and Au [51111/51111/5111]. The types of stationary points on potential energy surfaces were determined from analysis of Hessians. The second derivatives were calculated analytically. 

Early LSDA static pseudopotential approaches to sodium microclusters date back approximately 20 years [122], see Appendix C. It would be misleading to consider LDA calculations as the natural extension of jellium models. However, the global validity of the latter cannot but anticipate the success of the former. Clearly, these should also clarify the role of the atomic structure in determining the electronic behavior of the clusters and the extent to which the inhomogeneity of the electron distribution is reflected in the measurable properties. Many structural determinations are by now available for the smaller aggregates, made at different levels of approximation and of accuracy (e.g. [110, 111], see Appendix C). The most extensive investigation of sodium clusters so far is the LDA-CP study of Ref. [123] (see Appendix C), which makes use of all the features of the CP method. Namely, it uses dynamical SA to explore the potential-energy surface, MD to simulate clusters at different temperatures, and detailed analysis of the one-electron properties, which can be compared to the predictions of jellium-based models. 

Potential-energy surface obtained by varying the equatorial F-Te-F angle in TeF4. Calculations were run at the B3LYP level with aug-cc-pVTZ basis sets for Te and F. The core electrons on the Te have been replaced by a pseudopotential. Reproduced from [11] with permission of The Royal Society of Chemistry. 

All the reviewed programs carry out fundamental tasks of a computational chemist or a computational molecular physicist calculation of energy for various hamUtonians evaluation of gradients of energy (needed to locate stationary points on the potential energy surface) evaluation of the energy hessian (required to analyze the character of the located stationary point, identify local minima and saddle points, and perform vibrational frequency calculation) and evaluation of basic properties (population analysis, dipole moments). The components of the programs include basis set libraries and pseudopotentials. 

Most of the calculations have been done for Cu since it has the least number of electrons of the metals of interest. The clusters represent the Cu(100) surface and the positions of the metal atoms are fixed by bulk fee geometry. The adsorption site metal atom is usually treated with all its electrons while the rest are treated with one 4s electron and a pseudopotential for the core electrons. Higher z metals can be studied by using pseudopotentials for all the metals in the cluster. The adsorbed molecule is treated with all its electrons and the equilibrium positions are determined by minimizing the SCF energy. The positions of the adsorbate atoms are varied around the equilibrium position and SCF energies at several points are fitted to a potential surface to obtain the interatomic force constants and the vibrational frequency. 

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